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Plasmids are found across bacteria, archae … Plasmids are found across bacteria, archaea, and eukaryotes and play an important role in evolution. Plasmids exist at different copy numbers, the number of copies of the plasmid per cell, ranging from a single plasmid per cell to hundreds of plasmids per cell. This feature of a copy number greater than one can lead to a population of plasmids within a single cell that are not identical clones of one another, but rather have individual mutations that make a given plasmid unique. During cell division, this population of plasmids is partitioned into the two daughter cells, resulting in a random distribution of different plasmid variants in each daughter. In this study, we use stochastic simulations to investigate how random plasmid partitioning compares to a perfect partitioning model. Our simulation results demonstrate that random plasmid partitioning accelerates mutant allele fixation when the allele is beneficial and the selection is in an additive or recessive regime where increasing the copy number of the beneficial allele results in additional benefit for the host. This effect does not depend on the size of the benefit conferred or the mutation rate, but is magnified by increasing plasmid copy number.gnified by increasing plasmid copy number. +
Pre-orders on systems are the basis for ab … Pre-orders on systems are the basis for abstraction based verification of systems. In this paper, we investigate pre-orders for reasoning about stability with respect to inputs of hybrid systems. First, we present a superposition type theorem which gives a characterization of the classical incremental input-to-state stability of continuous systems in terms of the traditional epsilon/delta-definition of stability. We use this as the basis for defining a notion of incremental input- to-state stability of hybrid systems. Next, we present a pre-order on hybrid systems which preserves incremental input- to-state stability, by extending the classical definitions of bisimulation relations on systems with input, with uniform continuity constraints. We show that the uniform continuity is a necessary requirement by exhibiting counter-examples to show that weaker notions of input bisimulation with just continuity requirements do not suce to preserve stability. Finally, we demonstrate that the definitions are useful, by exhibiting concrete abstraction functions which satisfy the definitions of pre-orders.ich satisfy the definitions of pre-orders. +
Previous results in the use of pulsed air … Previous results in the use of pulsed air injection foractive control of rotating stall have suggested that air injectorshave the effect of shifting the steady state compressorcharacteristic. In this paper we analyze the effect of a compressorcharacteristic actuation scheme for the three state Moore Greitzercompression system model. It is shown that closed loop feedback basedon the square magnitude of the first rotating stall mode can be usedto decrease the hysteresis region associated with the transition fromunstalled to stalled and back to unstalled operation. The compressorcharacteristic shifting idea is then applied to a higher fidelitydistributed model in which the characteristic shifting has phasecontent in addition to the magnitude content captured by the threestate model. The optimal phasing of the air injection relative to thesensed position of the stall cell is determined via simulation and theresults found to agree with those obtained via an experimentalparametric study on the Caltech low-speed axial flow compressor.} Caltech low-speed axial flow compressor.} +
Previous work at Caltech has developed a c … Previous work at Caltech has developed a controller for rotating stallin axial flow compressors using pulsed air injection. In this work,theory is developed for the combination of this air injectioncontroller with a bleed valve controller for the system's surgedynamics. The controller analysis is based on the surge dynamicsacting on a slow time scale relative to the rotating stall dynamics.Experiments demonstrating this controller design on the Caltech rigare also presented.ign on the Caltech rig are also presented. +
Previous work at Caltech has developed an … Previous work at Caltech has developed an airinjection controller for rotating stall based on the idea of ashifting compressor characteristic. To further understand theproperties of this controllers, a series of open loop tests wereperformed to measure the performance characteristics of an axial flowcompression system when air was injected upstream of the rotor face.The distance from the rotor face, the span-wise position, and theangle relative to the mean axial flow were varied. These tests showthat the injection of air has drastic effects on the stalling massflow rate and on the size of the hysteresis loop associated withrotating stall. The stalling mass flow rate was decreased by 10\% andthe hysteresis loop was completely eliminated under some conditions.mpletely eliminated under some conditions. +
Quantifying performance of biomolecular ci … Quantifying performance of biomolecular circuit designs across different environmental conditions is a key step in assessing their robustness. It is generally unclear how robust this performance is to the important environmental variable of temperature. Here, we address this issue for a transcriptional negative feedback circuit design that can speed up the response time using a combination of simple computational methods and dynamic experimental measurements. We use a simple two-state model of gene expression to illustrate different ways in which temperature dependence of reaction rate parameters can propagate through to the functional output. Next, we extend this analysis to the response time of a transcriptional negative feedback circuit design. Finally, we present experimental results characterizing how response time of a negative transcriptional feedback circuit depends on temperature. These results help to develop framework for assessing how functional output of biomolecular circuit designs depend on temperature.lar circuit designs depend on temperature. +
RNA thermometers mediate responses to temp … RNA thermometers mediate responses to temperature changes in various natural circuits, and have been developed in a synthetic context as well. However, a toolbox of RNA thermometers with diâµerent sensitivities to temperature is lacking. Here, we address this issue using a combination of computational and experimental methodologies. We analysed a set of available synthetic RNA thermometers through a quantification of their activity as a function of temperatures in a cell- free expression molecular breadboard system as well as through computation of their melt profiles. Based on this, we computed melt profiles of a library of RNA thermometers and found that the library contained RNA thermometers with a range of sensitivities and thresholds in their response to temperature. We constructed this library and found, through preliminary measurements, a wide range of responses to temperature, which in some cases matched the computational predictions. The constructed library represents a toolbox of RNA thermometers with different sensitivities and is foun- dational work towards synthetic biology applications such as efficient control of large volume chemical reactors, precise spatiotemporal control of gene expression as well as tools to engineer robustness to temperature in biomolecular circuits.s to temperature in biomolecular circuits. +
Realizing homeostatic control of metabolit … Realizing homeostatic control of metabolites or proteins is one of the key goals of synthetic circuits. However, if control is only implemented internally in individual cells, cell-cell heterogeneity may break the homeostasis on population level since cells do not contribute equally to the production or regulation. New control structures are needed to achieve robust functionality in heterogeneous cell populations. Quorum sensing (QS) serves as a collective mechanism by releasing and sensing small and diffusible signaling molecules for group decision-making. We propose a layered feedback control structure that includes a global controller using quorum sensing and a local controller via internal signal-receptor systems. We demonstrate with modeling and simulation that the global controller drives contributing cells to compensate for disturbances while the local controller governs the fail-mode performance in non-contributing cells. The layered controller can tolerate a higher portion of non-contributing cells or longer generations of mutant cells while maintaining metabolites or proteins level within a small error range, compared with only internal feedback control. We further discuss the potential of such layered structures in robust control of cell population size, population fraction and other population-dependent functions. and other population-dependent functions. +
Receding horizon control allows a blending … Receding horizon control allows a blending of navigation and control functionsat the inner and outer loop levels and significantly enhances the ability of the controlsystem to react to complex dynamic and environmental constraints. In this paper, weexplore some of the limits of receding horizon control, including the extent to whichtraditional control specifications can be cast as RHC problem specifications. Simulationresults for a planar flight vehicle with representative flight dynamics illustratethe main features of the proposed approach.he main features of the proposed approach. +
Recent advances in geometric mechanics, mo … Recent advances in geometric mechanics, motivated in large part by applications incontrol theory, have introduced new tools for understanding and utilizing the structurepresent in mechanical systems. In particular, the use of geometric methods for analyzingLagrangian systems with both symmetries and non-integrable (or nonholonomic) constraintshas led to a unified formulation of the dynamics that has important implications for awide class of mechanical control systems. This paper presents a survey of recent resultsin this area, focusing on the relationships between geometric phases, controllability, andcurvature, and the role of trajectory generation in nonlinear controller synthesis.Examples are drawn from robotics and flight control systems, with an emphasis on motioncontrol problems.th an emphasis on motion control problems. +
Recent advances in nucleic acids engineeri … Recent advances in nucleic acids engineering introduced several RNA-based regulatory components for synthetic gene circuits, expanding the toolsets to engineer organisms. In this work, we designed genetic circuits implementing an RNA aptamer previously described to have the capability of binding to the T7 RNA polymerase and inhibiting its activity in vitro. Using in vitro transcription assays, we first demonstrated the utility of the RNA aptamer in combination with programmable synthetic transcription networks. As a step to quickly assess the feasibility of aptamer functions in vivo, a cell-free expression system was used as a breadboard to emulate the in vivo conditions of E. coli. We tested the aptamer and its three sequence variants in the cell-free expression system, verifying the aptamer functionality in the cell-free testbed. In vivo expression of aptamer and its variants demonstrated control over GFP expression driven by T7 RNA polymerase with different response curves, indicating its ability to serve as building blocks for both logic circuits and transcriptional cascades. This work elucidates the potential of RNA-based regulators for cell programming with improved controllability leveraging the fast production and degradation time scales of RNA molecules. degradation time scales of RNA molecules. +
Recent experimental results demonstrate th … Recent experimental results demonstrate that flies posses a robust tendency to orient towardsthe frontally-centered pole of the visual motion field that typically occurs during upwind flight.In this paper we present a closed loop flight model, with a control algorithm based on feedbackof the location of the visual pole of contraction, which is affected by changes in wind direction.The feasibility of visually guided upwind orientation is demonstrated with a model derivedfrom current understanding of the biomechanics and sensorimotor computation of insects. Thematched filter approach used to model the visual system computations compares extremely wellwith open-loop experimental data.ely well with open-loop experimental data. +
Recent work has introduced biocircuit arch … Recent work has introduced biocircuit architectures that exhibit robust oscillatory behavior in organisms ranging from cyanobacteria to mammals. Complementary research in synthetic biology has introduced oscillators in vivo and in vitro suggesting that robust oscillation can be recapitulated using a small number of biochemical components. In this work, we introduce signaling crosstalk in biocircuits as a consequence of enzyme-mediated biochemical reactions. As a motivating example, we consider an in vitro oscillator with two types of crosstalk: crosstalk in production and degradation of RNA signals. We then pose a framework for quantifying crosstalk and use it to derive several dynamical constraints and suggest design techniques for ameliorating crosstalk in in vitro biochemical systems. As an example, we show that the balance between production and degradation crosstalk plays a key role in determining system stability, potentially leading to loss of oscillatory behavior. We demonstrate that the effects of crosstalk can attenuated through the effective tuning of two key parameters in order to recover desired system dynamics. order to recover desired system dynamics. +
Reinforcement Learning (RL) algorithms hav … Reinforcement Learning (RL) algorithms have found limited success beyond simulated applications, and one main reason is the absence of safety guarantees during the learning process. Real world systems would realistically fail or break be- fore an optimal controller can be learned. To address this issue, we propose a controller architecture that combines (1) a model-free RL-based controller with (2) model-based controllers utilizing control barrier functions (CBFs) and (3) on- line learning of the unknown system dynamics, in order to ensure safety during learning. Our general framework lever- ages the success of RL algorithms to learn high-performance controllers, while the CBF-based controllers both guarantee safety and guide the learning process by constraining the set of explorable polices. We utilize Gaussian Processes (GPs) to model the system dynamics and its uncertainties.Our novel controller synthesis algorithm, RL-CBF, guaran- tees safety with high probability during the learning process, regardless of the RL algorithm used, and demonstrates greater policy exploration efficiency. We test our algorithm on (1) control of an inverted pendulum and (2) autonomous car-following with wireless vehicle-to-vehicle communication, and show that our algorithm attains much greater sample efficiency in learning than other state-of-the-art algorithms and maintains safety during the entire learning process.safety during the entire learning process. +
RoboFlag is a robotic version of capture t … RoboFlag is a robotic version of capture the flag that can be played either with autonomous controllers or with up to two humans in the loop. The goal of the game is to capture the flag of the other team, which is located in their defense zone, and bring it back to your home zone. The other team defends their flag by tagging your robots on their side of the field, at the same time as trying to capture your flag. Some of the interesting features of RoboFlag are that the robots have limited sensing capability and distributed processing, requiring that information be communicated between robots across limited bandwidth links. This makes the game much more challenging since you have two determine your actions without a complete view of the playing field.This paper gives an overview of the RoboFlag competition and describes some of the research challenges that are represented in the game.rch challenges that are represented in the game. +
Robot navigation in urban environments req … Robot navigation in urban environments requires situational reasoning. Given the complexity of the environment and the behavior specified by traffic rules, it is necessary to recognize the current situation to impose the correct traffic rules. In an attempt to manage the complexity of the situational reasoning subsystem, this paper describes a finite state machine model to govern the situational reasoning process. The logic state machine and its interaction with the planning system are discussed. The approach was implemented on Alice, Team Caltech's entry into the 2007 DARPA Urban Challenge. Results from the qualifying rounds are discussed. The approach is validated and the shortcomings of the implementation are identified.ings of the implementation are identified. +
Robotic locomotion is based in a variety o … Robotic locomotion is based in a variety of instances upon cyclic changes in the shapeof a robot mechanism. Certain variations in shape exploit the constrained nature of arobot's interaction with its environment to generate net motion. This is true for leggedrobots, snakelike robots, and wheeled mobile robots undertaking maneuvers such as parallelparking. In this paper we explore the use of tools from differential geometry to model andanalyze this class of locomotion mechanisms in a unified way. In particular, we describelocomotion in terms of the geometric phase associated with a connection on a principalbundle, and address issues such as controllability and choice of gait. We also provide anintroduction to the basic mathematical concepts which we require and apply the theory tonumerous example systems.ly the theory to numerous example systems. +
Robots with structural flexibility provide … Robots with structural flexibility provide an attractive alternativeto rigid robots for many of the new and evolving applications inrobotics. In certain applications their use is unavoidable. Theincreased complexity in modeling and control of such robots is offsetby desirable performance enhancements in some respects. In this thesiswe present a singular perturbation approach for modeling, analysis andcontrol of robots with flexibility. As our singular perturbationapproach does not treat the flexible manipulator as a perturbation ofthe rigid manipulator, it can treat significant flexibility, beyondthe linear range. Analysis based on this approach leads to someprovably stable control laws for the hybrid position and force controlof flexible-link manipulators. The analysis is done in the frameworkof a single robot manipulator in a constrained motiontask. Simulations and experimental results are presented for thiscase. To show applicability of the results to more general andcomplex systems with flexibilities we also present experimental datafrom a planar, two-fingered, reconfigurable grasping setup which allowsrigid and flexible configurations. The aim of the experimentation isto show the applicability of the control laws and analysis developed,and to determine the performance enhancements resulting from theintroduction of flexibility. Experimental data is analysed to show thetradeoffs between controller complexity and performance enhancement aswe deal with greater flexibility. Various performance criteria are setup and experimental results are discussed within their framework. Weconclude that large flexibility can be controlled without too muchadditional effort, has performance comparable to that of rigid robots,and possesses enhancing properties which make it appealing for use incertain types of applications. for use in certain types of applications. +
Robustness to temperature variation is an … Robustness to temperature variation is an important specification in biomolecular circuit design. While the cancellation of parametric temperature dependencies has been shown to improve the temperature robustness of the period in a synthetic oscillator design, the performance of other biomolecular circuit designs in different temperature conditions is relatively unclear. Using a combination of experimental measurements and mathematical models, we assessed the temperature robustness of two biomolecular circuit motifs—a negative feedback loop and a feedforward loop. We found that the measured responses of both the circuits changed with temperature, both in the amplitude and in the transient response. We also found that, in addition to the cancellation of parametric temperature dependencies, certain parameter regimes could facilitate the temperature robustness of the negative feedback loop, although at a performance cost. We discuss these parameter regimes in the context of the measured data for the negative feedback loop. These results should help develop a framework for assessing and designing temperature robustness in biomolecular circuits.ature robustness in biomolecular circuits. +
Rotating stall and surge are aerodynamic i … Rotating stall and surge are aerodynamic instabilities that limit the performance ofaeroengines. A set of magnetic bearings supporting the compressor rotor is a potentialactuator for active control of rotating stall and surge. Based on a first-principles modelwe show that using this type of actuation, the first harmonic mode of rotating stall islinearly controllable, but the second harmonic mode and the surge mode are linearlyuncontrollable. We then give an explicit procedure for designing feedback laws such thatthe first mode is linearly stabilized and the criticality of the Hopf bifurcations of thesecond mode and the surge mode are supercritical. We also investigate the effects ofmagnitude saturation on the regions of attraction. We demonstrate the theoretical resultsby numerical simulations of a model for a transonic compressor at the NASA Lewis ResearchCenter.pressor at the NASA Lewis Research Center. +
Rules or specifications for autonomous veh … Rules or specifications for autonomous vehicles are currently formulated on a case-by-case basis, and put together in a rather ad-hoc fashion. As a step towards eliminating this practice, we propose a systematic procedure for generating a set of supervisory specifications for self-driving cars that are 1) associated with a distributed assume-guarantee structure and 2) characterizable by the notion of consistency and completeness. Besides helping autonomous vehicles make better decisions on the road, the assume-guarantee contract structure also helps address the notion of blame when undesirable events occur. We give several game-theoretic examples to demonstrate applic bility of our framework.emonstrate applic bility of our framework. +
Safe and robust G&C (Guidance and Cont … Safe and robust G&C (Guidance and Control) algorithms for onboard implementation are developed by augmenting a model predictive control technique with a safety mode. The application example herein is spacecraft small-body proximity operations where model and constraint uncertainty warrant G&C algorithms with a degree of autonomous, onboard decision capability. The algorithm enforces state and control constraints and merges two operational modes: (I) standard mode guides the spacecraft to the proximity of a target state in a robust and resolvable model-predictive manner; (II) safety mode, if activated, maintains the spacecraft near a safety reference for all time. The algorithm utilizes separate feedforward and feedback components. In standard mode, the feedforward guidance solutions come from a way-point generation algorithm that uses a discrete linear-time-varying dynamics model. This approach provides a convex formulation of the problem (solvable onboard as a second-order cone program) that includes control and state constraints; the safety-mode availability adds a constraint in this standard-mode formulation as well. The feedback guarantees standard-mode resolvability to update the guidance profile in a robust, model-predictive manner. In safety mode, an offline-designed feedforward policy with the added feedback maintains the spacecraft in a hovering state in the proximity of its position at safety-mode activation time; this provides robustness to unexpected state-constraint changes such as unexpected ground proximity during landing operations. A simulation demonstrating both the standard and safety modes is provided for a spacecraft autonomous-descent scenario toward a small asteroid with an uncertain gravity model and errors in the surface altitude constraint.del and errors in the surface altitude constraint. +
Safety guarantees are built into a robust … Safety guarantees are built into a robust MPC (Model Predictive Control) algorithm for uncertain nonlinear systems. The algorithm is designed to obey all state and control constraints and blend two operational modes: (I) standard mode guarantees resolvability and asymptotic convergence to the origin in a robust receding-horizon manner; (II) safety mode, if activated, guarantees containment within an invariant set about a safety reference for all time. This research is motivated by physical vehicle control-algorithm design (e.g. spacecraft and hovercraft) in which operation mode changes must be considered. Incorporating safety mode provides robustness to unexpected state-constraint changes; e.g., other vehicles crossing/stopping in the feasible path, or unexpected ground proximity in landing scenarios. The safety-mode control is provided by an offline designed control policy that can be activated at any arbitrary time during standard mode. The standard-mode control consists of separate feedforward and feedback components; feedforward comes from online solution of a FHC (Finite-Horizon optimal Control problem), while feedback is designed offline to generate an invariant tube about the feedforward tra jectory. The tube provides robustness (to uncertainties and disturbances in the dynamics) and guarantees FHC resolvability. The algorithm design is demonstrated for a class of systems with uncertain nonlinear terms that have norm-bounded Jacobians.ar terms that have norm-bounded Jacobians. +
Serine integrases are bacteriophage protei … Serine integrases are bacteriophage proteins responsible for integrating the phage genome into that of the host. Synthetic biologists have co-opted these proteins into useful tools for permanent DNA logic, utilizing their specific DNA recombination abilities to build synthetic cell differentiation and genetic memory systems. Each integrase has a specific pair of DNA sequences (attP/attB sites) that it recombines, but multiple identical sites can result in unpredictable recombination. We have developed a way to control integrase activity on identical attP/attB sites by using catalytically dead Cas9 (dCas9) as a programmable binding protein that can compete with integrase for binding to specific attachment sites. Utilizing a plasmid that contains two identical Bxb1 attP sites, integration can be repressed up to 8 fold at either one of the two attP sites when guide RNA and dCas9 are present. Guide RNA sequences that bind specifically to attB, or either of two attP sites, have been developed. Future goals are to utilize this technology to construct larger and more complex integrase logic circuits.and more complex integrase logic circuits. +
Single-cell bacterial sensors have numerou … Single-cell bacterial sensors have numerous applications in human health monitoring, environmental chemical detection, and materials biosynthesis. Many previous efforts for synthetic bacteria strains seek to optimize homogenous single cell behavior. Rather than attempt to reduce noise in circuit behavior, we take advantage of heterogenous single cell responses to record sequences of chemical events within a population. Using an engineered E. coli strain with a 4-state temporal logic gate, we show, both in silico and in vivo, that stochastic digital switching within single cells results in an analog population fractionation that can be used to resolve inducer pulse duration within 30 minutes. Furthermore, these results are preserved in the genome and can be read out at a time that is much later than the time of the event. is much later than the time of the event. +
Specifications for complex engineering sys … Specifications for complex engineering systems are typically decomposed into specifications for individual subsystems in a manner that ensures they are implementable and simpler to develop further. We describe a method to algorithmically construct component specifications that implement a given specification when assembled. By eliminating variables that are irrelevant to realizability of each component, we simplify the specifications and reduce the amount of information necessary for operation. We parametrize the information flow between components by introducing parameters that select whether each variable is visible to a component or not. The decomposition algorithm identifies which variables can be hidden while pre- serving realizability and ensuring correct composition, and these are eliminated from component specifications by quantification and conversion of binary decision diagrams to formulas. The resulting specifications describe component viewpoints with full information with respect to the remaining variables, which is essential for tractable algorithmic synthesis of implementations. The specifications are written in TLA+, with liveness properties restricted to an implication of conjoined recurrence properties, known as GR(1). We define an operator for forming open systems from closed systems, based on a variant of the “while-plus” operator. This operator simplifies the writing of specifications that are realizable without being vacuous. To convert the generated specifications from binary decision diagrams to readable formulas over integer variables, we symbolically solve a minimal covering problem. We show with examples how the method can be applied to obtain contracts that formalize the hierarchical structure of system design.e hierarchical structure of system design. +
Standard schemes in system identification … Standard schemes in system identification and adaptive control rely on persistence of excitation to guaran- tee parameter convergence. Inspired by networked systems, we extend parameter adaptation to the multi-agent setting by combining a gradient law with consensus dynamics. The gradient law introduces a learning signal, while consensus dynamics preferentially push each agentâs parameter estimates toward those of its neighbors. We show that the resulting online, decentralized parameter estimator combines local and neighboring information to identify the true parameters even if no single agent employs a persistently exciting input. We also elaborate upon collective persistence of excitation in networked adaptive algorithms.citation in networked adaptive algorithms. +
Station keeping and reorientation control … Station keeping and reorientation control of a cluster of fully-actuated low-thrust micro-satellites is considered in this paper. We address the control problem by taking advantage of the fully-actuated structure of the micro-satellite. We propose a very general open-loop solution by solving in real-time constrained trajectory generation problems for stationkeeping and reorientation. Performance of this methodology is reported for a typical micro-satellite format ion flying space mission using the Nonlinear Trajectory Generation software package.ar Trajectory Generation software package. +
Stochastic gene expression poses an import … Stochastic gene expression poses an important challenge for engineering robust behaviors in a heterogeneous cell population. Cells address this challenge by operating on distributions of cellular responses generated by noisy processes. Similarly, a previously published temporal logic gate considers the distribution of responses across a cell population under chemical inducer pulsing events. The design uses a system of two integrases to engineer an E. coli strain with four DNA states that records the temporal order of two chemical signal events. The heterogeneous cell population response was used to infer the timing and duration of the two chemical signals for a small set of events. Here we use the temporal logic gate system to address the problem of extracting information about chemical signal events. We use the heterogeneous cell population response to infer whether any event has occurred or not and also to infer its properties such as timing and amplitude. Bayesian inference provides a natural framework to answer our questions about chemical signal occurrence, timing, and amplitude. We develop a probabilistic model that incorporates uncertainty in the how well our model captures the cell population and in how well a sample of measured cells represents the entire population. Using our probabilistic model and cell population measurements taken every five minutes on generated data, we ask how likely it was to observe the data for parameter values that describe square-shaped inducer pulses. We compare the likelihood functions associated with the probabilistic models for the event with the chemical signal pulses turned on versus turned off. Hence, we can determine whether an event of chemical induction of integrase expression has occurred or not. Using Markov Chain Monte Carlo, we sample the posterior distribution of chemical pulse parameters to identify likely pulses that produce the data measurements. We implement this method and obtain accurate results for detecting chemical inducer pulse timing, length, and amplitude. We can detect and identify chemical inducer pulses as short as half an hour, as well as all pulse amplitudes that fall under biologically relevant conditions.ll under biologically relevant conditions. +
Stochasticity plays an essential role in b … Stochasticity plays an essential role in biochemical systems. Stochastic behaviors of bimodality, excitability, and fluctuations have been observed in biochemical reaction networks at low molecular numbers. Stochastic dynamics can be captured by modeling the system using a forward Kolmogorov equation known in the biochemical literature as the chemical master equation. The chemical master equation describes the time evolution of the probability distributions of the molecule species. We develop a stochastic framework for the design of these time evolving probability distributions that includes specifying their uni-/multi-modality, their first moments, and their rate of convergence to the stationary distribution. By solving the corresponding optimizations programs, we determine the reaction rates of the biochemical systems that satisfy our design specifications. We then apply the design framework to examples of biochemical reaction networks to illustrate its strengths and limitations. illustrate its strengths and limitations. +
Substantial reductions in aircraft size a … Substantial reductions in aircraft size are possible if shorter, more aggressive, serpentine inlet ducts are used for low-observability constrained propulsion installations. To obtain this benefit, both inlet separation and compressor stall dynamics must be controlled. In this paper the integrated control of this coupled inlet/compression system is considered. Initial results are shown using separation point actuation to control both separation and stall dynamics. Calculations show that separation can be substantially reduced with approximately 1.2% core flow, based on scaling previous results. Simulation results using a medium fidelity model show that proportional control of distortion has little effect on stall behavior.tion has little effect on stall behavior. +
Successful high-speed autonomous navigatio … Successful high-speed autonomous navigation requires integration of tools from robotics, control theory, computer vision, and systems engineering. This thesis presents work that develops and combines these tools in the context of navigating desert terrain.A comparative analysis of reactive, behavior-based, and deliberative control architectures provides important guidelines for design of robotic systems. These guidelines depend on the particular task and environment of the vehicle. Two important factors are identified which guide an effective choice between these architectures: dynamic feasibility for the vehicle, and predictability of the environment. This is demonstrated by parallels to control theory, illustrative examples, simulations, and analysis of Bob and Alice---Caltech's full-scale autonomous ground vehicle entries in the 2004 and 2005 Grand Challenge races, respectively.Further, new model-based methods are developed for constructing and maintaining estimates of terrain elevation and road geometry. These are demonstrated in simulation and in fully autonomous operation of Alice, including accurate detection and tracking of the centerline of desert roads at speeds up to 5 m/s. Finally, Alice's navigation architecture is presented in full along with experimental results that demonstrate its capabilities.results that demonstrate its capabilities. +
Synthetic biologists have turned towards q … Synthetic biologists have turned towards quorum systems as a path for building sophisticated microbial consortia that exhibit group decision making. Currently, however, even the most complex consortium circuits rely on only one or two quorum sensing systems, greatly restricting the available design space. High-throughput characterization of available quorum sensing systems is useful for finding compatible sets of systems that are suitable for a defined circuit architecture. Recently, cell-free systems have gained popularity as a test-bed for rapid prototyping of genetic circuitry. We take advantage of the transcription-translation cell-free system to characterize three commonly used Lux-type quorum activators, Lux, Las, and Rpa. We then compare the cell-free characterization to results obtained in vivo. We find significant genetic crosstalk in both the Las and Rpa systems and substantial signal crosstalk in Lux activation. We show that cell-free characterization predicts crosstalk observed in vivo.ation predicts crosstalk observed in vivo. +
Synthetic gene expression is highly sensit … Synthetic gene expression is highly sensitive to intragenic compositional context (promoter structure, spacing regions between promoter and coding sequences, and ribosome binding sites). However, much less is known about the effects of intergenic compositional context (spatial arrangement and orientation of entire genes on DNA) on expression levels in synthetic gene networks. We compare expression of induced genes arranged in convergent, divergent, or tandem orientations. Induction of convergent genes yielded up to 400% higher expression, greater ultrasensitivity, and dynamic range than divergent- or tandem-oriented genes. Orientation affects gene expression whether one or both genes are induced. We postulate that transcriptional interference in divergent and tandem genes, mediated by supercoiling, can explain differences in expression and validate this hypothesis through modeling and in vitro supercoiling relaxation experiments. Treatment with gyrase abrogated intergenic context effects, bringing expression levels within 30% of each other. We rebuilt the toggle switch with convergent genes, taking advantage of supercoiling effects to improve threshold detection and switch stability. threshold detection and switch stability. +
Synthetic gene networks are frequently con … Synthetic gene networks are frequently conceptualized and visualized as static graphs. This view of biological programming stands in stark contrast to the transient nature of biomolecular interaction, which is frequently enacted by labile molecules that are often unmeasured. Thus, the network topology and dynamics of synthetic gene networks can be difficult to verify in vivo or in vitro, due to the presence of unmeasured biological states. Here we introduce the dynamical structure function as a new mesoscopic, data-driven class of models to describe gene networks with incomplete measurements. We introduce a network reconstruction algorithm and a code base for reconstructing the dynamical structure function from data, to enable discovery and visualization of graphical relationships in a genetic circuit diagram as time-dependent functions rather than static, unknown weights. We prove a theorem, showing that dynamical structure functions can provide a data-driven estimate of the size of crosstalk fluctuations from an idealized model. We illustrate this idea with numerical examples. Finally, we show how data-driven estimation of dynamical structure functions can explain failure modes in two experimentally implemented genetic circuits, a historical genetic circuit and a new E. coli based transcriptional event detector.coli based transcriptional event detector. +
Synthetic transcriptional networks built f … Synthetic transcriptional networks built from CRISPR-based repressors (CRISPRi) rely on shared use of a core dCas9 protein. In E. coli, CRISPRi cannot support more than about a dozen simultaneous gRNAs before the fold repression of any individual gRNA drops below 10x. We show with a simple model based on previous characterization of competition in CRISPRi that activation by CRISPR-based activators (CRISPRa) is much less sensitive to dCas9 bottle-necking than CRISPRi. We predict that E. coli should be able to support dozens to hundreds of CRISPRa gRNAs at >10-fold activation.s of CRISPRa gRNAs at >10-fold activation. +
Targeted transcriptional repression with c … Targeted transcriptional repression with catalytically inactive Cas9 (CRISPRi) can be used to build gene regulatory nets similar in principle to those made with traditional transcription factors, and promises to do so with better orthogonality, programmability, and extensibility. We use a simple dynamical model of CRISPRi to understand its behavior and requirements, and to show that CRISPRi can recapitulate several classic gene regulatory circuits, including the repressilator, a toggle switch, and an incoherent feed-forward loop pulse generator. Our model also predicts that these circuits are highly sensitive to promoter leak, but that promoter leak can be offset with active degradation of dCas. We provide specifications for required fold-repression and dCas degradation rates for several dynamic circuits. Our modeling reveals key engineering requirements and considerations for the construction of dynamic CRISPRi circuits, and provides a roadmap for building those circuits.des a roadmap for building those circuits. +
Temporal dynamics in many biomolecular cir … Temporal dynamics in many biomolecular circuits can change with temperature because of the temperature dependence of underlying reaction rate parameters. It is generally unclear what circuit mechanisms can inherently facilitate robustness in the dynamics to variations in temperature. Here, we address this issue using a combination of mathematical models and experimental measure- ments in a cell-free transcription-translation system. We find that negative transcriptional feedback can reduce the eâµect of temperature variation on circuit dynamics. Further, we find that effective negative feedback due to first-order degradation mechanisms can also enable such a temperature robustness effect. Finally, we estimate temperature dependence of key parameters mediating such negative feedback mechanisms. These results should be useful in the design of temperature robust circuit dynamics.gn of temperature robust circuit dynamics. +
Temporal logic based synthesis approaches … Temporal logic based synthesis approaches are often used to find trajectories that are correct-by-construction in systems–eg. synchronization for multi-agent hybrid systems, reactive motion planning for robots. However, the scalability of such approaches is of concern and at times a bottleneck when transitioning from theory to practice. In this paper, we identify a class of problems in the GR(1) fragment of linear-time temporal logic (LTL) where the synthesis problem allows for a decomposition that enables easy parallelization. This decomposition also reduces the alternation depth, resulting in more efficient synthesis. A multi-agent robot gridworld example with coordination tasks is presented to demonstrate the application of the developed ideas and also to perform empirical analysis for benchmarking the decomposition-based synthesis approach.he decomposition-based synthesis approach. +
Temporal logics have proven effective for … Temporal logics have proven effective for correct-by-constructionsynthesis of controllers for a wide range ofapplications. Receding horizon frameworks mitigate thecomputational intractability of reactive synthesis for temporallogic, but have thus far been limited by pursuing a singlesequence of short horizon problems to the current goal. Wepropose a receding horizon algorithm for reactive synthesis thatautomatically determines a path to the currently pursued goal atruntime, in response to a nondeterministic environment. This isachieved by allowing each short horizon to have multiple localgoals, and determining which local goal to pursue based on thecurrent global goal, currently perceived environment and apre-computed invariant dependent on each global goal. Wedemonstrate the utility of this additional flexibility ingrant-response tasks, using a search-and-rescueexample. Moreover, we show that these goal-dependent invariantsmitigate the conservativeness of the receding horizon approach.tiveness of the receding horizon approach. +
The Caltech Multi Vehicles Wireless Testbe … The Caltech Multi Vehicles Wireless Testbed (MVWT)is a platform designed to explore theoritical advancesin multi-vehicle coordination and control, networkedcontrol systems and high con�dence distributedcomputation. The contribution of this report is topresent simulation and experimental results on thegeneration and implementation of optimal trajectoriesfor the MVWT vehicles. The vehicles are nonlinearand spatially contrained with bounded input control.The trajectories are generated using the NTG softwarepackage developed at Caltech. Minimum time trajectoriesand the application of Model Predictive Control (MPC)are investigated.can actually follow i.e. trajectories that satisfy everyconstraint of the testbed. Those constraints can eitherbe linear, like the boundaries of the testbed or nonlinearlike the constraints on the input. The main di�erence andalso di�culty in our case is that the system is not linearlycontrollable around its equilibrium.In Section 2 we will give a quick description of the systemsproperties and in Section 3 and 4 we will describe theprogression which led us from the optimization problemto the implementation on the real vehicles. In Section5 other optimization problems such as minimum timetrajectory generation and model predictive control areinvestigated.model predictive control are investigated. +
The Caltech Multi-Vehicle Wireless Testbed … The Caltech Multi-Vehicle Wireless Testbed isan experimental platform for validating theoretical advancesin multiple-vehicle coordination and cooperation, real-timenetworked control system, and distributed computation. Thispaper describes the design and development of an additionalfleet of 12 second-generation vehicles. These vehicles arehovercrafts and designed to have lower mass and friction aswell as smaller size than the first generation vehicles. Thesehovercrafts combined with the outdoor wireless testbed providea perfect hardware platform for RoboFlag competition.ardware platform for RoboFlag competition. +
The Electrostatically Suspended Gyroscope … The Electrostatically Suspended Gyroscope (ESG) is a two-axis inertial orientati onsensor manufactured by Boeing and currently in use on U.S. Navy submarines. The additional ability of the ESG to act as an accelerometer is well known, but extraction ofprecision acceleration measuremen ts from an ESG has not been achieved. The majorobstacles to precision accelerometry are the nonlinear dynamics of the ESG rotor and parametric variation of the ESG electronics. In this paper, we derive a model for the ESGdynamics with an eye toward efficient representation of the uncertainties in the model. Werepresent the model uncert ainties and nonlinearities in a framework amenable tomu-analysis and analyze ESG accelerometer precision using $\mu$-analysis tools. Finally,we discuss the implementation of a digital ESG control architecture for use in ESG systemidentification and testing of suspension control and acce lerometer algorithms.ion control and acce lerometer algorithms. +
The Goursat normal form theorem gives cond … The Goursat normal form theorem gives conditions under which anPfaffian exterior differential system is equivalent to a certainnormal form. This paper details how the Goursat normal form and itsextensions provide a unified framework for understanding feedbacklinearization, chained form, and differential flatness. Keywords: Exterior differential systems, nonholonomic constraints,chained form, feedback linearization, differentially flat.rm, feedback linearization, differentially flat. +
The One-Pot PURE system for in vitro prote … The One-Pot PURE system for in vitro protein expression, which results from a co-culture and one-step purification of 36 essential proteins to support gene transcription and translation, can significantly improve the accessibility and affordability of PURE systems. However, replicating this protocol to match the productivity of the traditional PURE system can take considerable time and effort due to variability in the expression level of individual proteins. In this work, we observed unstable PURE protein expression in two E. coli protein expression strains, M15/pREP4 and BL21(DE3), and addressed this instability using catabolite repression. We identified key proteins whose concentration in the One-Pot PURE mixture significantly impacted the reaction’s protein expression capacity. Compared to the original method using two E. coli protein expression strains, we found that consolidating all expression vectors onto one BL21 (DE3) strain led to more uniform cell growth at the time of protein induction, thereby improving the composition of critical translation initiation factors in the purified mixture for efficient translation. We also found that variations in commercial energy solution formulations could compensate for deficiencies in the One-Pot PURE protein composition. Additionally, our study revealed significant differences in the translation capacity of commercially available E. coli tRNAs, suggesting the potential of optimizing tRNA composition to improve protein translation. Taken together, this work highlights the intricate biochemical interplay influencing protein expression capacity in the One-Pot PURE system and presents strategies to improve its robustness and productivity.o improve its robustness and productivity. +
The Python Control Systems Library (python … The Python Control Systems Library (python-control) is an open source set of Python classes and functions that implement common operations for the analysis and design of feedback control systems. In addition to support for standard LTI control systems (including time and frequency response, block diagram algebra, stability and robustness analysis, and control system synthesis), the package provides support for nonlinear input/output systems, including system interconnection, simulation, and describing function analysis. A MATLAB compatibility layer provides an many of the common functions corresponding to commands available in the MATLAB Control Systems Toolbox. The library takes advantage of the Python “scientific stack” of Numpy, Matplotlib, and Jupyter Notebooks and offers easy interoperation with other category-leading software systems in data science, machine learning, and robotics that have largely been built on Python.cs that have largely been built on Python. +
The T7 bacteriophage RNA polymerase (T7 RN … The T7 bacteriophage RNA polymerase (T7 RNAP) serves as a model for understanding RNA synthesis, as a tool for protein expression, and as an actuator for synthetic gene circuit design in bacterial cells and cell-free extract. T7 RNAP is an attractive tool for orthogonal protein expression in bacteria owing to its compact single subunit structure and orthogonal promoter specificity. Understanding the mechanisms underlying T7 RNAP regulation is important to the design of engineered T7-based transcription factors, which can be used in gene circuit design. To explore regulatory mechanisms for T7 RNAP-driven expression, we developed a rapid and cost-effective method to characterize engineered T7-based transcription factors using cell-free protein synthesis and an acoustic liquid handler. Using this method, we investigated the effects of the tetracycline operator’s proximity to the T7 promoter on the regulation of T7 RNAP-driven expression. Our results reveal a mechanism for regulation that functions by interfering with the transition of T7 RNAP from initiation to elongation and validates the use of the method described here to engineer future T7-based transcription factors.eer future T7-based transcription factors. +
The ability to guarantee safety and progre … The ability to guarantee safety and progress for all vehicles is vital to the success of the autonomous vehicle industry. We present a framework for designing autonomous vehicle behavior in a way that is safe and guarantees progress for all agents. In this paper, we first introduce a new game paradigm which we term the quasi-simultaneous game. We then define an agent protocol that all agents must use to make decisions in this quasi-simultaneous game setting. According to the protocol, agents first select an intended action using a behavioral profile. Then, the protocol defines whether an agent has precedence to take its intended action or must take a sub-optimal action. The protocol ensures safety under all traffic conditions and liveness for all agents under `sparse' traffic conditions. We provide proofs of correctness of the protocol and validate our results in simulation.ol and validate our results in simulation. +
The ability to rapidly design, build, and … The ability to rapidly design, build, and test prototypes is of key importance to every engineering discipline. DNA assembly often serves as a rate limiting step of the prototyping cycle for synthetic biology. Recently developed DNA assembly methods such as isothermal assembly and type IIS restriction enzyme systems take different approaches to accelerate DNA construction. We introduce a hybrid method, Golden Gate-Gibson (3G), that takes advantage of modular part libraries introduced by type IIS restriction enzyme systems and isothermal assembly's ability to build large DNA constructs in single pot reactions. Our method is highly efficient and rapid, facilitating construction of entire multi-gene circuits in a single day. Additionally, 3G allows generation of variant libraries enabling efficient screening of different possible circuit constructions. We characterize the efficiency and accuracy of 3G assembly for various construct sizes, and demonstrate 3G by characterizing variants of an inducible cell-lysis circuit.riants of an inducible cell-lysis circuit. +
The acrobot is a simple mechanical system … The acrobot is a simple mechanical system patterned after a gymnastperforming on a single parallel bar. By swinging her legs, a gymnastis able to bring herself into an inverted position with her center ofmass above the part and is able to perform manuevers about thisconfiguration. This report studies the use of nonlinear controltechniques for designing a controller to operate in a neighborhood ofthe manifold of inverted equilibrium points. The techniques describedhere are of particular interest because the dynamic model of theacrobot violates many of the necessary conditions required to applycurrent methods in linear and nonlinear control theory.The approach used in this report is to approximate the system in sucha way that the behavior of the system about the manifold ofequilibrium points is correctly captured. In particular, we constructan approximating system which agrees with the linearization of theoriginal system on the equilibrium manifold and is full statelinearizable. For this class of approximations, controllers can beconstructed using recent techniques from differential geometric control theory. We show that application of control laws derived in thismanner results in approximate trajectory tracking for the system undercertain restrictions on the class of desired trajectories. Simulationresults based on a simplified model of the acrobot are included. a simplified model of the acrobot are included. +

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